Optimal Control of a Mathematical Model for Monkeypox Transmission in Indonesia Using the Pontryagin Maximum Principle - Musfira, Musfira; Side, Syafruddin; Abdy, Muhammad; Ridho, Andi Muhammad; Supriadi, Supriadi (Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Negeri Makassar, 2025)
Abstract: The re-emergence of Monkeypox poses significant public health challenges in Indonesia. This disease continues to spread due to its zoonotic nature and the high frequency of human-animal interactions. This study aims to model the transmission dynamics of Monkeypox using the SIQR (Susceptible, Infectious, Quarantined, Recovered) framework and apply optimal control strategies through the Pantryagin Maximum Principle (PMP). Data from the Indonesian Ministry of Health were utilised for model parameterisation, with numerical simulations conducted using the fourth-order Runge-Kutta method. Control strategies included quarantine, tecovirimat, and public education. The simulation results revealed that implementing optimal control reduced the infected population by up to 75% within the first 10 months compared to scenarios without control. The basic reproduction number () was successfully reduced from 2.5 to below 1, indicating that the outbreak was controlled. Additionally, the recovery rate increased by 30%, with the susceptible population achieving a disease-free equilibrium by the eighth month. These findings highlight that mathematically-driven interventions can provide effective solutions for managing infectious diseases. It is recommended that these strategies be integrated into public health policies to optimise resource allocation. Further research is necessary to evaluate the scalability of this approach for other zoonotic diseases.